Extraction of Correlated Sparse Sources from Signal Mixtures

A blind source separation method is described to extract sources from data mixtures where the underlying sources are sparse and correlated. The approach used is to detect and analyze segments of time where one source exists on its own. The method does not assume independence of sources and probability density functions are not assumed for any of the sources. A comparison is made between the proposed method and the Fast-ICA and Clusterwise PCA methods. It is shown that the proposed method works best for cases where the underlying sources are strongly correlated because Fast-ICA assumes zero correlation between sources and Clusterwise PCA can be sensitive to overlap between sources. However, for cases of sources that are sparse and weakly correlated with each other, there is a tendency for Fast-ICA and Clusterwise PCA to have better performances than the proposed method, the reason being that these methods appear to be more robust to changes in input parameters to the algorithms. In addition, because of the deflationary nature of the proposed method, there is a tendency for estimates to be more affected by noise than Fast-ICA when the number of sources increases. The paper concludes with a discussion concerning potential applications for the proposed method. 1. Introduction One general problem in signal processing is the extraction of individual source signals from measurements that are linear combinations of these sources: where are the mixing coefficients, is the number of sets of measurement data, and there are underlying sources. In the case where both the sources and mixing coefficients are unknown, this problem comes under the heading of blind source separation (BSS). There are many applications in this area [1–8]. There are various approaches to extracting the underlying sources . For example, in Independent Component Analysis (ICA), the aim is to determine a transformation of the data that maximizes the negentropy [9]. In the approach designed in [10], the aim is to minimize the cross-cumulants. Now in some applications, the underlying sources can be approximated as sparse; that is, each source has nonzero values for a finite segment of time, with the other sources having zero values. In practice, this definition can be approximated by each source being dominant over other sources for at least one segment of time. Various specialized BSS methods have been derived for the case of sparse sources [11–18]. In one approach [12], the sparsity of a signal is defined over data points by Assuming two sources, the aim is to find a transformation on the data